Question

verify that the equations are identities:
1+cosy/1-cosy = sin^2y/(1-cos^2y)

Answer 1

Hint: sin^2y = 1 - cos^2y

Answer 2

I'm going to show you my steps, although, it might not be the way you learned how to do these.

Answer 3

I worked through it and got 1-cos^2y/1-cos^y

Answer 4

I don't believe it is an identity according to my math

Answer 5

this is how I done it 1-cos^2y/(1-cos^2y)(1+cos^2y)= 1-cos^2y/1-cos^2y

Answer 6

I'm telling you that I don't believe the identity is true

Answer 7

I can show you my work. It's pretty simple

Answer 8

How do you decide which side to start on?

Answer 9

I'll show you what I did

Answer 10

I knew that sin^2y = 1 - cos^2y so I substituted that in:

\(\large\frac{1+cos x}{1-cos x} = \frac{1-cos^2x}{1-cos^2x} \)

Answer 11

Now look at the right side. It cancels to 1

Answer 12

So you have

\(\large\frac{1 + cos x}{1-cos x} = 1\)

Answer 13

Now you multiply both sides by 1 - cos x to get

1 + cos x = 1 - cos x

Answer 14

and now you can see that \(1 + cos x \ne 1 - cos x\)

Answer 15

so the identity is false

Answer 16

thanks